If you find you need more control over the image, a DSLR camera can be used, though the learning curve is higher. A point-and-shoot camera of good quality is generally sufficient for recording simple video like you talking into a microphone. Although you can use your webcam, those tend to have grainy pictures and do not provide the highest quality. If you want a video of yourself on screen, you'll need some way to capture it.
Let's take a look at what all goes into recording a screen. For example, if you want to have a video of yourself in the corner of the screen, you'll need a camera set up in addition to your audio recording equipment. This applies not only to the audio portion but to other areas as well.
How you approach recording your screen depends on what you are trying to do.